Question

11. A circle is given by the equation (x^2+2x+1)+(y^2+4y+4)=121.

a. What is the center of the circle?
b. What is the radius of the circle?
c. Describe what you had to do in order to determine the center and the radius of the circle.

Answer 1

a) the centre of the circle is at point (h,k) = (-1,-2)

b) the radius of the circle is r = 11

c) we need to factorize each of the equation and write it in the form of the standard equation of a circle the we will compare to the standard equation of circle so as to get the values of the radius and the centre.

Explanation:

Given;

Equation of the circle is

(x^2+2x+1) + (y^2+4y+4)=121

To determine the centre and radius of the circle we need to factorize each of the equation to give the

(x-h)^2 + (y-k)^2 = r^2 ......1

This is the standard form of a circle. We will then use this form to determine the center and radius of the circle. By Matching the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

Factorizing the equation of the circle we have;

(x+1)^2 + (y+2)^2 = 11^2 ....2

Comparing equation 2 to 1

We have;

h = -1

k = -2

r = 11

Therefore,

a) the centre of the circle is at point (h,k) = (-1,-2)

b) the radius of the circle is r = 11

c) we need to factorize each of the equation and write it in the form of the standard equation of a circle the we will compare to the standard equation of circle so as to get the values of the radius and the centre.